Show that if the vector field F = Pi + Qj + Rk is conservative and P, Q, R have continuous first-order partial derivatives, then the following is true. ∂P ∂y = ∂Q ∂x ∂P ∂z = ∂R ∂x ∂Q ∂z = ∂R ∂y . Since F is conservative, there exists a function f such that F = ∇f, that is, P, Q, and R are defined as follows. (Enter your answers in the form fx, fy, fz.) P = Q = R = Since P, Q, and R have continuous first order partial derivatives, says that ∂P/∂y = fxy = fyx = ∂Q/∂x, ∂P/∂z = fxz = fzx = ∂R/∂x, and ∂Q/∂z = fyz = fzy = ∂R/∂y.

Katlyn made 4 dresses with 7 yards of fabric. how many yards did she use on 1 dress?

Sophia wrote an equation to represent the revenue of a movie theater for one day. she let x represent the number of child tickets sold and y represents the nunver of adult tickets sold. if a child ticket cost $4, an adult ticket cost $6, and the total revenue for the daybwas $420, which equation could sophia use to represent the number of chikd and adult tickets that were sold?

Aresearch study is studying the effects of a new drug for osteoporosis alzheimer's disease (ad) for women above the age of 65 years. a group of individuals with osteoporosis is randomized into two groups. one group is treated conventionally, and the second group is treated with the new medication. assessments are made at 3, 6, 12, 36, and 48 months. the conventionally treated group is assessed for ad using a serum blood test, and the treatment group is assessed for ad using a pet radiotracer that binds to beta-amyloid plaques. in comparing these 2 trial arms, the authors of the study may encounter which type of bias? a. selection bias on the risk of developing b. measurement bias c. confounding bias d. recall bias e. lead-time bias